Rockfish Historical Harvest Estimates

This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: rf_harvest_est_kha_rm_wt_thru2023_1e+05_7kn_2025-05-29 (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.8731

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Model fit

Logbook residuals

Figure 18.- Residuals from logbook harvests.

SWHS residuals

Figure 19.- Residuals from SWHS harvests.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 21.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

## NULL

## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Weight Fits

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

### Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.

parameter n badRhat_avg beta1_pH 25 2.088164 beta3_pelagic 5 2.039699 mu_beta0_pH 1 1.950667 beta0_pelagic 5 1.759294 beta1_pelagic 6 1.629222 beta0_pH 16 1.625122 sd_comp 1 1.572617 beta0_yellow 6 1.465212 beta1_yellow 6 1.448821 beta3_pH 19 1.390111

parameter n badRhat_avg beta3_yellow 4 1.383979 beta4_pelagic 4 1.380567 beta2_pelagic 7 1.329802 tau_beta0_pH 1 1.319404 beta2_pH 28 1.271140 beta2_yellow 5 1.243258 mu_beta0_yellow 1 1.171901 tau_beta0_yellow 1 1.151724 beta_H 1 1.121530

##   [1] "mu3_wt"         "re_dsr"         "sd3_wt"         "beta1_pH"      
##   [5] "re_pelagic"     "re_pH"          "beta0_pH"       "mu_beta1_pH"   
##   [9] "Ro_ay"          "beta3_pH"       "Rdnye_ay"       "Rdnye_ay_mort" 
##  [13] "p_dsr"          "mu_beta0_pH"    "Tdnye_ay"       "p_pelagic"     
##  [17] "pH"             "Bdnye_ay"       "Hd_ayg"         "Rs_ay"         
##  [21] "Rs_ay_mort"     "Rdnye_ayg"      "Rdnye_ayg_mort" "Ro_ayg"        
##  [25] "Ry_ay"          "Ry_ay_mort"     "Ty_ay"          "Bdnye_ayu"     
##  [29] "Tdnye_ayu"      "By_ay"          "Ro_ayu"         "Rdnye_ayu_mort"
##  [33] "Rdnye_ayu"      "Rs_ayu"         "Rs_ayu_mort"    "mu2_wt"        
##  [37] "re_yellow"      "Ts_ay"          "Ts_ayu"         "Bs_ayu"        
##  [41] "beta2_pH"       "beta4_pH"       "Hp_ay"          "Ry_ayu"        
##  [45] "Ry_ayu_mort"    "Hb_ay"          "Rs_ayg"         "Rs_ayg_mort"   
##  [49] "Tdnye_ayg"      "mu_beta2_pH"    "Hp_ayu"         "Hb_ayu"        
##  [53] "Bdnye_ayg"      "Ty_ayu"         "By_ayu"         "Tp_ayu"        
##  [57] "Bp_ayu"         "Tb_ayu"         "Bb_ayu"         "Bs_ay"         
##  [61] "sd2_wt"         "Tp_ay"          "Tb_ay"          "Ry_ayg"        
##  [65] "Ry_ayg_mort"    "Hp_ayg"         "Hb_ayg"         "Hd_ay"         
##  [69] "Bp_ay"          "tau_beta0_pH"   "Bb_ay"          "Hy_ayg"        
##  [73] "Rp_ay"          "Rp_ay_mort"     "Rp_ayg"         "Rp_ayg_mort"   
##  [77] "Tp_ayg"         "R_ayg"          "R_ay"           "Rb_ay"         
##  [81] "Rb_ay_mort"     "Rb_ayg"         "Rb_ayg_mort"    "Bp_ayg"        
##  [85] "Tb_ayg"         "Bb_ayg"         "Rb_ayu"         "Rb_ayu_mort"   
##  [89] "Rp_ayu"         "Rp_ayu_mort"    "R_ayu"          "Ty_ayg"        
##  [93] "By_ayg"         "Rd_ayg"         "Rd_ay"          "tau_beta1_pH"  
##  [97] "Rd_ayu"         "pDSR_YE_ay"     "p_yellow"       "pDSR_YE_ayu"   
## [101] "Hdnye_ay"       "H_ayu"          "Hy_ay"          "H_ay"          
## [105] "Hy_ayu"         "Ts_ayg"         "Hd_ayu"         "pDSR_YE_ayg"   
## [109] "Hdnye_ayg"      "Ho_ayg"         "Hdnye_ayu"      "Ho_ayu"        
## [113] "Bs_ayg"         "Ho_ay"          "mu_beta4_pH"    "tau_beta2_pH"  
## [117] "Hs_ayu"         "logbc_R"        "logRhat_ayg"    "Htrend_ay"     
## [121] "beta_H"         "re_rslope"      "H_ayg"

Table 3. Summary of unconverged parameters by area

variable	afognak	BSAI	CI	CSEO	eastside	EWYKT	NG	northeast	NSEI	NSEO	PWSI	PWSO	SOKO2SAP	SSEI	SSEO	WKMA
beta_H	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
beta0_pH	0	0	0	2	1	3	0	1	3	1	0	0	1	1	2	1
beta1_pH	1	1	1	1	1	3	1	1	3	2	2	2	2	1	2	1
beta2_pH	1	1	1	3	1	3	1	1	3	3	1	1	1	3	3	1
beta3_pH	1	0	1	3	0	2	1	0	2	3	0	0	0	3	2	1
beta4_pH	0	0	0	2	0	2	0	0	0	1	1	0	0	0	0	0
Bp_ay	0	0	0	24	0	8	0	0	13	9	0	0	0	11	12	0
Bp_ayg	0	0	0	21	0	9	0	0	13	10	0	0	0	10	11	0
Bp_ayu	0	0	0	26	0	8	0	0	9	8	0	0	0	9	7	0
H_ay	1	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0
H_ayg	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
H_ayu	0	3	0	0	0	0	0	0	0	0	0	0	0	0	1	0
Hb_ay	0	3	0	26	0	0	0	0	0	0	0	0	0	0	0	0
Hb_ayg	0	0	0	21	0	0	0	0	0	0	0	0	0	0	0	0
Hb_ayu	0	3	0	27	0	0	0	0	0	0	0	0	0	0	0	0
Hd_ay	0	0	0	22	0	0	0	0	0	0	0	0	0	0	0	0
Hd_ayg	0	0	0	12	0	0	0	0	0	1	0	0	0	0	0	0
Hd_ayu	0	0	0	3	0	0	0	0	0	0	0	0	0	0	1	0
Hdnye_ay	0	0	0	6	0	0	0	0	0	2	0	0	0	0	0	0
Hdnye_ayg	0	0	0	4	0	0	0	0	0	1	0	0	0	0	0	0
Hdnye_ayu	0	0	0	4	0	0	0	0	0	0	0	0	0	0	0	0
Ho_ay	0	2	0	13	0	0	0	0	0	0	0	0	0	0	0	0
Ho_ayg	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Ho_ayu	1	1	0	2	2	0	0	0	0	0	0	0	0	0	0	0
Hp_ay	1	3	0	27	0	0	0	0	0	0	0	0	0	0	0	0
Hp_ayg	2	0	0	21	0	0	0	0	0	0	0	0	0	0	0	0
Hp_ayu	0	3	0	27	0	0	0	0	0	0	0	0	0	0	0	0
Hs_ayu	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
Htrend_ay	9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Hy_ay	0	0	0	2	0	0	0	0	0	1	0	0	0	0	3	0
Hy_ayg	0	0	0	1	0	0	0	0	0	0	0	0	0	0	2	0
Hy_ayu	0	1	0	1	0	0	0	0	0	0	0	0	0	0	3	0
logbc_R	0	0	0	3	0	0	0	0	0	0	0	0	0	0	0	0
logRhat_ayg	0	0	0	3	0	0	0	0	0	0	0	0	0	0	0	0
mu_beta0_pH	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
mu_beta1_pH	0	0	1	0	0	0	1	0	0	0	2	0	0	0	0	0
mu_beta2_pH	0	0	1	0	0	0	1	0	0	0	3	0	0	0	0	0
mu_beta4_pH	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
p_dsr	0	0	0	70	0	4	0	0	0	2	0	0	0	0	0	0
p_pelagic	0	0	0	50	0	0	0	0	0	0	0	0	0	0	0	0
p_yellow	0	0	0	3	0	0	0	0	0	5	0	0	0	0	4	0
pDSR_YE_ay	0	0	0	3	0	0	0	0	0	4	0	0	0	0	2	0
pDSR_YE_ayg	0	0	0	2	0	0	0	0	0	2	0	0	0	0	2	0
pDSR_YE_ayu	0	0	0	1	0	0	0	0	0	3	0	0	0	0	2	0
pH	0	0	0	138	3	123	2	0	35	107	0	0	0	26	29	7
R_ay	11	12	11	18	9	12	10	12	12	8	11	12	18	11	11	11
R_ayg	10	16	11	13	10	9	12	13	13	9	10	12	16	10	10	12
R_ayu	10	14	11	11	8	17	10	10	10	11	10	14	17	11	11	12
Rb_ay	12	14	12	16	10	8	10	12	17	9	11	13	19	11	12	15
Rb_ay_mort	12	14	12	16	10	8	10	12	17	9	12	12	19	11	12	14
Rb_ayg	9	16	12	14	10	9	12	12	16	10	13	12	16	11	10	14
Rb_ayg_mort	9	16	12	14	10	9	12	12	16	10	13	12	16	11	10	14
Rb_ayu	13	13	10	17	7	13	10	10	15	10	13	14	19	10	12	13
Rb_ayu_mort	13	13	10	17	7	13	10	10	15	10	13	14	19	10	12	13
Rd_ay	0	0	0	6	0	7	0	0	3	7	0	0	0	4	3	0
Rd_ayg	0	0	0	2	0	17	0	0	5	10	0	0	0	9	8	0
Rd_ayu	0	0	0	6	0	7	0	0	0	2	0	0	0	4	2	0
Rdnye_ay	0	0	0	40	0	46	0	0	4	42	0	0	0	17	17	0
Rdnye_ay_mort	0	0	0	40	0	46	0	0	4	42	0	0	0	17	17	0
Rdnye_ayg	0	0	0	25	0	29	0	0	7	29	0	0	0	19	8	0
Rdnye_ayg_mort	0	0	0	25	0	29	0	0	7	29	0	0	0	19	8	0
Rdnye_ayu	0	0	0	40	0	46	0	0	3	45	0	0	0	10	13	0
Rdnye_ayu_mort	0	0	0	40	0	46	0	0	3	45	0	0	0	10	13	0
re_pelagic	0	0	0	41	0	0	0	0	30	12	21	16	0	10	5	0
re_pH	1	0	0	64	27	54	2	26	53	30	0	0	11	21	33	27
re_rslope	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
Ro_ay	3	7	3	40	4	46	1	1	3	45	0	3	4	21	19	3
Ro_ayg	4	9	2	27	4	29	3	3	9	29	4	3	2	18	8	9
Ro_ayu	2	7	3	40	5	46	0	1	3	45	0	4	4	10	15	3
Rp_ay	12	13	11	17	9	8	10	12	18	10	12	14	19	11	12	12
Rp_ay_mort	12	15	11	17	9	8	10	12	18	10	11	13	19	11	12	12
Rp_ayg	10	16	11	14	10	9	12	13	16	10	10	13	16	10	10	12
Rp_ayg_mort	10	16	11	14	10	9	12	13	16	10	10	13	16	10	10	12
Rp_ayu	12	14	11	18	8	13	10	10	16	12	11	14	19	11	12	13
Rp_ayu_mort	12	14	11	18	8	13	10	10	16	12	11	14	19	11	12	13
Rs_ay	0	0	0	40	0	41	0	0	3	45	0	0	0	14	14	0
Rs_ay_mort	0	0	0	40	0	42	0	0	3	45	0	0	0	14	14	0
Rs_ayg	0	0	0	23	0	29	0	0	2	26	0	0	0	15	3	0
Rs_ayg_mort	0	0	0	23	0	29	0	0	2	26	0	0	0	15	3	0
Rs_ayu	0	0	0	40	0	46	0	0	3	45	0	0	0	5	12	0
Rs_ayu_mort	0	0	0	40	0	46	0	0	3	45	0	0	0	5	12	0
Ry_ay	18	21	10	46	22	21	4	23	5	23	0	6	31	5	14	8
Ry_ay_mort	18	21	10	46	22	21	4	23	5	23	0	6	31	5	14	8
Ry_ayg	16	10	12	18	16	15	12	16	21	20	9	7	12	5	20	9
Ry_ayg_mort	16	10	12	18	16	15	12	16	21	20	9	7	12	5	20	9
Ry_ayu	15	25	9	46	19	18	2	23	1	10	0	4	31	2	15	8
Ry_ayu_mort	15	25	9	46	19	18	2	23	1	10	0	4	31	2	15	8
tau_beta0_pH	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
tau_beta1_pH	0	0	1	0	0	0	1	0	0	0	1	0	0	0	0	0
tau_beta2_pH	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
Tp_ay	11	11	11	26	9	8	7	12	12	9	10	10	12	11	11	11
Tp_ayg	10	12	11	22	10	9	6	13	13	10	10	11	16	10	10	11
Tp_ayu	10	12	8	26	7	11	3	10	9	10	4	5	11	9	8	12

##  [1] CI        NG        PWSI      PWSO      BSAI      SOKO2SAP  WKMA     
##  [8] afognak   eastside  northeast CSEO      EWYKT     NSEI      NSEO     
## [15] SSEI      SSEO     
## 16 Levels: CI < NG < PWSI < PWSO < BSAI < SOKO2SAP < WKMA < ... < SSEO

Table 2. Summary of unconverged major parameters by area

Parameter	CI	NG	PWSI	PWSO	BSAI	SOKO2SAP	WKMA	afognak	eastside	northeast	CSEO	EWYKT	NSEI	NSEO	SSEI	SSEO
beta_H	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
beta_H	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
beta0_pH	0	0	0	0	0	1	1	0	1	1	2	3	3	1	1	2
beta0_pH	0	0	0	0	0	1	1	0	1	1	1	1	1	1	1	1
beta1_pH	1	1	2	2	1	2	1	1	1	1	1	3	3	2	1	2
beta1_pH	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
beta2_pH	1	1	1	1	1	1	1	1	1	1	3	3	3	3	3	3
beta2_pH	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
beta3_pH	1	1	0	0	0	0	1	1	0	0	3	2	2	3	3	2
beta3_pH	1	1	0	0	0	0	1	1	0	0	1	1	1	1	1	1
beta4_pH	0	0	1	0	0	0	0	0	0	0	2	2	0	1	0	0
Bp_ay	0	0	0	0	0	0	0	0	0	0	24	8	13	9	11	12
Bp_ayg	0	0	0	0	0	0	0	0	0	0	21	9	13	10	10	11
Bp_ayu	0	0	0	0	0	0	0	0	0	0	26	8	9	8	9	7
H_ay	0	0	0	0	3	0	0	1	0	0	0	0	0	0	0	0
H_ayg	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
H_ayu	0	0	0	0	3	0	0	0	0	0	0	0	0	0	0	1
Hb_ay	0	0	0	0	3	0	0	0	0	0	26	0	0	0	0	0
Hb_ayg	0	0	0	0	0	0	0	0	0	0	21	0	0	0	0	0
Hb_ayu	0	0	0	0	3	0	0	0	0	0	27	0	0	0	0	0
Hd_ay	0	0	0	0	0	0	0	0	0	0	22	0	0	0	0	0
Hd_ayg	0	0	0	0	0	0	0	0	0	0	12	0	0	1	0	0
Hd_ayu	0	0	0	0	0	0	0	0	0	0	3	0	0	0	0	1
Hdnye_ay	0	0	0	0	0	0	0	0	0	0	6	0	0	2	0	0
Hdnye_ayg	0	0	0	0	0	0	0	0	0	0	4	0	0	1	0	0
Hdnye_ayu	0	0	0	0	0	0	0	0	0	0	4	0	0	0	0	0
Ho_ay	0	0	0	0	2	0	0	0	0	0	13	0	0	0	0	0
Ho_ayg	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	0
Ho_ayu	0	0	0	0	1	0	0	1	2	0	2	0	0	0	0	0
Hp_ay	0	0	0	0	3	0	0	1	0	0	27	0	0	0	0	0
Hp_ayg	0	0	0	0	0	0	0	2	0	0	21	0	0	0	0	0
Hp_ayu	0	0	0	0	3	0	0	0	0	0	27	0	0	0	0	0
Hs_ayu	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
Htrend_ay	0	0	0	0	0	0	0	9	0	0	0	0	0	0	0	0
Hy_ay	0	0	0	0	0	0	0	0	0	0	2	0	0	1	0	3
Hy_ayg	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	2
Hy_ayu	0	0	0	0	1	0	0	0	0	0	1	0	0	0	0	3
logbc_R	0	0	0	0	0	0	0	0	0	0	3	0	0	0	0	0
logRhat_ayg	0	0	0	0	0	0	0	0	0	0	3	0	0	0	0	0
mu_beta0_pH	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
mu_beta0_pH	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
mu_beta1_pH	1	1	2	0	0	0	0	0	0	0	0	0	0	0	0	0
mu_beta2_pH	1	1	3	0	0	0	0	0	0	0	0	0	0	0	0	0
mu_beta4_pH	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
p_dsr	0	0	0	0	0	0	0	0	0	0	70	4	0	2	0	0
p_pelagic	0	0	0	0	0	0	0	0	0	0	50	0	0	0	0	0
p_yellow	0	0	0	0	0	0	0	0	0	0	3	0	0	5	0	4
pDSR_YE_ay	0	0	0	0	0	0	0	0	0	0	3	0	0	4	0	2
pDSR_YE_ayg	0	0	0	0	0	0	0	0	0	0	2	0	0	2	0	2
pDSR_YE_ayu	0	0	0	0	0	0	0	0	0	0	1	0	0	3	0	2
pH	0	2	0	0	0	0	7	0	3	0	138	123	35	107	26	29
R_ay	11	10	11	12	12	18	11	11	9	12	18	12	12	8	11	11
R_ayg	11	12	10	12	16	16	12	10	10	13	13	9	13	9	10	10
R_ayu	11	10	10	14	14	17	12	10	8	10	11	17	10	11	11	11
Rb_ay	12	10	11	13	14	19	15	12	10	12	16	8	17	9	11	12
Rb_ay_mort	12	10	12	12	14	19	14	12	10	12	16	8	17	9	11	12
Rb_ayg	12	12	13	12	16	16	14	9	10	12	14	9	16	10	11	10
Rb_ayg_mort	12	12	13	12	16	16	14	9	10	12	14	9	16	10	11	10
Rb_ayu	10	10	13	14	13	19	13	13	7	10	17	13	15	10	10	12
Rb_ayu_mort	10	10	13	14	13	19	13	13	7	10	17	13	15	10	10	12
Rd_ay	0	0	0	0	0	0	0	0	0	0	6	7	3	7	4	3
Rd_ayg	0	0	0	0	0	0	0	0	0	0	2	17	5	10	9	8
Rd_ayu	0	0	0	0	0	0	0	0	0	0	6	7	0	2	4	2
Rdnye_ay	0	0	0	0	0	0	0	0	0	0	40	46	4	42	17	17
Rdnye_ay_mort	0	0	0	0	0	0	0	0	0	0	40	46	4	42	17	17
Rdnye_ayg	0	0	0	0	0	0	0	0	0	0	25	29	7	29	19	8
Rdnye_ayg_mort	0	0	0	0	0	0	0	0	0	0	25	29	7	29	19	8
Rdnye_ayu	0	0	0	0	0	0	0	0	0	0	40	46	3	45	10	13
Rdnye_ayu_mort	0	0	0	0	0	0	0	0	0	0	40	46	3	45	10	13
re_pelagic	0	0	21	16	0	0	0	0	0	0	41	0	30	12	10	5
re_pH	0	2	0	0	0	11	27	1	27	26	64	54	53	30	21	33
re_rslope	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0
Ro_ay	3	1	0	3	7	4	3	3	4	1	40	46	3	45	21	19
Ro_ayg	2	3	4	3	9	2	9	4	4	3	27	29	9	29	18	8
Ro_ayu	3	0	0	4	7	4	3	2	5	1	40	46	3	45	10	15
Rp_ay	11	10	12	14	13	19	12	12	9	12	17	8	18	10	11	12
Rp_ay_mort	11	10	11	13	15	19	12	12	9	12	17	8	18	10	11	12
Rp_ayg	11	12	10	13	16	16	12	10	10	13	14	9	16	10	10	10
Rp_ayg_mort	11	12	10	13	16	16	12	10	10	13	14	9	16	10	10	10
Rp_ayu	11	10	11	14	14	19	13	12	8	10	18	13	16	12	11	12
Rp_ayu_mort	11	10	11	14	14	19	13	12	8	10	18	13	16	12	11	12
Rs_ay	0	0	0	0	0	0	0	0	0	0	40	41	3	45	14	14
Rs_ay_mort	0	0	0	0	0	0	0	0	0	0	40	42	3	45	14	14
Rs_ayg	0	0	0	0	0	0	0	0	0	0	23	29	2	26	15	3
Rs_ayg_mort	0	0	0	0	0	0	0	0	0	0	23	29	2	26	15	3
Rs_ayu	0	0	0	0	0	0	0	0	0	0	40	46	3	45	5	12
Rs_ayu_mort	0	0	0	0	0	0	0	0	0	0	40	46	3	45	5	12
Ry_ay	10	4	0	6	21	31	8	18	22	23	46	21	5	23	5	14
Ry_ay_mort	10	4	0	6	21	31	8	18	22	23	46	21	5	23	5	14
Ry_ayg	12	12	9	7	10	12	9	16	16	16	18	15	21	20	5	20
Ry_ayg_mort	12	12	9	7	10	12	9	16	16	16	18	15	21	20	5	20
Ry_ayu	9	2	0	4	25	31	8	15	19	23	46	18	1	10	2	15
Ry_ayu_mort	9	2	0	4	25	31	8	15	19	23	46	18	1	10	2	15
tau_beta0_pH	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
tau_beta0_pH	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
tau_beta1_pH	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0
tau_beta2_pH	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
Tp_ay	11	7	10	10	11	12	11	11	9	12	26	8	12	9	11	11
Tp_ayg	11	6	10	11	12	16	11	10	10	13	22	9	13	10	10	10
Tp_ayu	8	3	4	5	12	11	12	10	7	10	26	11	9	10	9	8
beta0_pelagic	0	0	1	1	0	0	0	0	0	0	1	0	1	0	0	1
beta0_yellow	0	0	0	1	0	0	0	0	0	0	1	1	0	1	1	1
beta1_pelagic	0	0	1	1	0	0	0	0	0	0	1	0	1	1	1	0
beta1_yellow	0	0	0	1	0	0	0	0	0	0	1	1	0	1	1	1
beta2_pelagic	0	0	1	1	0	0	0	0	0	0	1	0	1	1	1	1
beta2_yellow	0	1	1	0	0	0	0	0	0	0	1	0	0	1	1	0
beta3_pelagic	0	0	1	1	0	0	0	0	0	0	1	0	0	1	0	1
beta3_yellow	0	0	0	0	0	0	0	0	0	0	1	0	0	1	1	1
beta4_pelagic	0	0	0	0	1	1	0	0	1	0	1	0	0	0	0	0
mu_beta0_yellow	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
sd_comp	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
tau_beta0_yellow	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.158	0.068	-0.288	-0.160	-0.021
mu_bc_H[2]	-0.128	0.036	-0.194	-0.129	-0.053
mu_bc_H[3]	-0.452	0.074	-0.590	-0.451	-0.305
mu_bc_H[4]	-1.077	0.207	-1.497	-1.071	-0.681
mu_bc_H[5]	0.697	0.820	-0.334	0.536	2.726
mu_bc_H[6]	-2.187	0.319	-2.802	-2.194	-1.550
mu_bc_H[7]	-0.481	0.111	-0.709	-0.481	-0.265
mu_bc_H[8]	0.129	0.346	-0.410	0.085	0.892
mu_bc_H[9]	-0.351	0.139	-0.627	-0.349	-0.070
mu_bc_H[10]	-0.156	0.066	-0.281	-0.156	-0.024
mu_bc_H[11]	-0.145	0.039	-0.224	-0.144	-0.071
mu_bc_H[12]	-0.281	0.112	-0.520	-0.272	-0.074
mu_bc_H[13]	-0.217	0.076	-0.362	-0.218	-0.062
mu_bc_H[14]	-0.349	0.106	-0.569	-0.344	-0.153
mu_bc_H[15]	-0.370	0.053	-0.473	-0.372	-0.264
mu_bc_H[16]	-0.677	0.358	-1.340	-0.695	0.053
mu_bc_R[1]	1.511	0.159	1.205	1.513	1.833
mu_bc_R[2]	1.524	0.085	1.358	1.525	1.690
mu_bc_R[3]	1.445	0.148	1.157	1.449	1.725
mu_bc_R[4]	1.099	0.184	0.718	1.106	1.438
mu_bc_R[5]	1.612	0.499	0.605	1.618	2.588
mu_bc_R[6]	-1.086	0.526	-2.097	-1.087	-0.049
mu_bc_R[7]	0.441	0.154	0.130	0.442	0.736
mu_bc_R[8]	0.614	0.193	0.228	0.619	0.979
mu_bc_R[9]	0.549	0.166	0.207	0.553	0.851
mu_bc_R[10]	1.512	0.145	1.236	1.514	1.795
mu_bc_R[11]	1.063	0.106	0.858	1.061	1.283
mu_bc_R[12]	0.915	0.195	0.548	0.910	1.308
mu_bc_R[13]	1.103	0.107	0.904	1.100	1.323
mu_bc_R[14]	0.958	0.143	0.673	0.959	1.235
mu_bc_R[15]	0.871	0.123	0.641	0.867	1.129
mu_bc_R[16]	1.162	0.129	0.909	1.161	1.417
tau_pH[1]	0.189	0.204	0.040	0.088	0.747
tau_pH[2]	1.656	0.609	0.251	1.846	2.453
tau_pH[3]	1.624	0.610	0.578	1.843	2.557
beta0_pH[1,1]	4.164	1.542	1.901	4.270	7.196
beta0_pH[2,1]	7.048	2.333	2.966	7.099	10.723
beta0_pH[3,1]	4.930	2.244	1.938	4.658	9.203
beta0_pH[4,1]	5.300	2.022	2.477	5.290	9.517
beta0_pH[5,1]	2.119	1.118	0.308	1.922	4.460
beta0_pH[6,1]	1.712	1.183	0.045	1.462	4.448
beta0_pH[7,1]	2.359	1.264	0.481	1.989	4.307
beta0_pH[8,1]	2.826	1.590	0.265	3.084	5.169
beta0_pH[9,1]	2.243	1.297	0.615	2.070	5.637
beta0_pH[10,1]	4.279	1.814	1.523	4.286	7.128
beta0_pH[11,1]	7.752	2.450	2.861	7.782	11.879
beta0_pH[12,1]	3.429	1.197	1.979	3.054	5.945
beta0_pH[13,1]	5.583	2.523	1.654	4.871	10.020
beta0_pH[14,1]	3.803	1.665	1.503	3.588	6.948
beta0_pH[15,1]	6.559	2.429	2.088	7.018	10.159
beta0_pH[16,1]	5.002	2.043	1.546	4.976	8.807
beta0_pH[1,2]	2.860	0.198	2.478	2.862	3.254
beta0_pH[2,2]	2.869	0.176	2.535	2.866	3.214
beta0_pH[3,2]	3.122	0.183	2.791	3.116	3.517
beta0_pH[4,2]	2.988	0.180	2.681	2.974	3.438
beta0_pH[5,2]	4.597	1.388	2.840	4.301	8.207
beta0_pH[6,2]	3.174	0.269	2.706	3.155	3.787
beta0_pH[7,2]	1.869	0.228	1.418	1.871	2.309
beta0_pH[8,2]	2.862	0.222	2.453	2.860	3.314
beta0_pH[9,2]	3.488	0.285	2.970	3.473	4.145
beta0_pH[10,2]	3.756	0.250	3.250	3.758	4.241
beta0_pH[11,2]	-3.546	2.491	-5.576	-4.776	3.579
beta0_pH[12,2]	-4.344	1.171	-5.489	-4.673	-0.687
beta0_pH[13,2]	-4.051	1.486	-5.430	-4.525	0.913
beta0_pH[14,2]	-4.828	1.500	-6.392	-5.220	0.361
beta0_pH[15,2]	-3.645	1.691	-5.041	-4.294	1.293
beta0_pH[16,2]	-4.290	1.568	-5.657	-4.761	0.905
beta0_pH[1,3]	-0.315	0.781	-1.814	-0.314	1.181
beta0_pH[2,3]	2.193	0.213	1.764	2.196	2.604
beta0_pH[3,3]	2.543	0.180	2.186	2.541	2.920
beta0_pH[4,3]	2.975	0.195	2.608	2.967	3.391
beta0_pH[5,3]	1.134	0.717	0.137	1.032	2.855
beta0_pH[6,3]	0.568	0.608	-0.611	0.599	1.693
beta0_pH[7,3]	0.620	0.204	0.212	0.621	1.012
beta0_pH[8,3]	0.317	0.238	-0.144	0.315	0.798
beta0_pH[9,3]	-0.467	0.456	-1.471	-0.455	0.393
beta0_pH[10,3]	0.549	0.434	-0.539	0.597	1.256
beta0_pH[11,3]	0.486	1.077	-0.991	0.574	2.187
beta0_pH[12,3]	0.117	1.310	-1.539	-0.565	2.100
beta0_pH[13,3]	0.389	0.832	-0.878	0.347	1.571
beta0_pH[14,3]	0.373	0.851	-0.932	0.099	1.696
beta0_pH[15,3]	0.237	1.497	-1.636	0.354	4.816
beta0_pH[16,3]	0.143	0.825	-1.219	-0.014	1.394
beta1_pH[1,1]	0.240	0.492	0.000	0.004	1.693
beta1_pH[2,1]	0.674	0.985	0.000	0.071	3.815
beta1_pH[3,1]	0.245	0.444	0.000	0.005	1.386
beta1_pH[4,1]	0.324	0.624	0.000	0.007	2.020
beta1_pH[5,1]	0.204	0.473	0.000	0.000	1.710
beta1_pH[6,1]	0.140	0.343	0.000	0.000	1.196
beta1_pH[7,1]	1.386	2.013	0.000	0.000	5.213
beta1_pH[8,1]	0.249	0.407	0.000	0.000	1.176
beta1_pH[9,1]	0.168	0.677	0.000	0.000	1.168
beta1_pH[10,1]	0.207	0.426	0.000	0.000	1.423
beta1_pH[11,1]	0.005	0.021	0.000	0.000	0.058
beta1_pH[12,1]	0.011	0.054	0.000	0.000	0.119
beta1_pH[13,1]	0.055	0.263	0.000	0.000	1.207
beta1_pH[14,1]	0.030	0.201	0.000	0.000	0.204
beta1_pH[15,1]	0.008	0.033	0.000	0.000	0.104
beta1_pH[16,1]	0.007	0.031	0.000	0.000	0.065
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.000	0.001	0.000	0.000	0.001
beta1_pH[4,2]	0.000	0.001	0.000	0.000	0.001
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	5.507	2.162	0.123	6.538	7.536
beta1_pH[12,2]	6.026	1.225	2.166	6.333	7.295
beta1_pH[13,2]	6.325	1.696	0.297	6.854	7.867
beta1_pH[14,2]	6.450	1.601	1.004	6.855	8.101
beta1_pH[15,2]	5.967	2.011	0.064	6.757	7.634
beta1_pH[16,2]	6.747	1.878	0.147	7.307	8.335
beta1_pH[1,3]	4.935	1.831	1.465	4.963	8.659
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	3.594	4.269	0.870	2.652	14.785
beta1_pH[6,3]	3.427	7.578	0.455	2.101	21.889
beta1_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,3]	2.671	0.526	1.793	2.639	3.661
beta1_pH[9,3]	2.634	0.532	1.680	2.607	3.919
beta1_pH[10,3]	2.671	0.606	1.652	2.613	4.156
beta1_pH[11,3]	1.682	1.524	0.000	1.877	3.728
beta1_pH[12,3]	2.528	2.037	0.000	3.706	4.927
beta1_pH[13,3]	1.004	0.922	0.000	1.208	2.422
beta1_pH[14,3]	1.542	1.269	0.000	2.085	3.364
beta1_pH[15,3]	1.071	1.084	0.000	0.706	2.884
beta1_pH[16,3]	1.058	0.969	0.000	1.310	2.589
beta2_pH[1,1]	-2.102	8.354	-17.883	-1.008	15.418
beta2_pH[2,1]	-2.179	7.848	-18.455	-0.659	15.015
beta2_pH[3,1]	-1.867	8.278	-18.946	-1.038	14.977
beta2_pH[4,1]	-1.777	8.454	-19.023	-0.702	15.423
beta2_pH[5,1]	2.638	10.153	-6.301	0.412	32.861
beta2_pH[6,1]	2.534	10.226	-6.061	0.326	34.084
beta2_pH[7,1]	11.165	43.074	0.000	0.001	129.997
beta2_pH[8,1]	3.014	10.093	-5.601	0.771	34.442
beta2_pH[9,1]	2.560	10.218	-6.078	0.394	32.747
beta2_pH[10,1]	2.460	10.233	-5.997	0.145	32.848
beta2_pH[11,1]	-0.971	7.354	-14.701	-0.139	13.856
beta2_pH[12,1]	-0.765	7.556	-15.924	-0.091	14.716
beta2_pH[13,1]	-0.813	7.170	-15.966	0.050	14.213
beta2_pH[14,1]	-0.769	7.621	-15.959	0.071	14.845
beta2_pH[15,1]	-0.885	7.536	-15.977	-0.277	14.238
beta2_pH[16,1]	-0.707	7.568	-15.497	0.013	14.456
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	-2.008	1.821	-6.789	-1.564	-0.028
beta2_pH[4,2]	-1.953	1.783	-6.552	-1.490	-0.029
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	-8.874	5.695	-24.125	-7.549	-1.056
beta2_pH[12,2]	-7.987	5.963	-24.413	-6.323	-1.175
beta2_pH[13,2]	-7.938	5.876	-23.774	-6.310	-1.500
beta2_pH[14,2]	-8.373	5.782	-24.040	-6.715	-2.052
beta2_pH[15,2]	-8.927	5.555	-23.748	-7.325	-2.320
beta2_pH[16,2]	-8.805	5.631	-24.374	-6.711	-1.914
beta2_pH[1,3]	0.181	0.191	0.100	0.129	0.531
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	8.799	6.304	0.373	7.761	23.309
beta2_pH[6,3]	8.668	6.510	0.139	7.556	24.040
beta2_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,3]	9.346	6.245	0.534	8.249	24.311
beta2_pH[9,3]	8.801	6.448	0.486	7.578	25.043
beta2_pH[10,3]	8.330	6.692	0.395	7.132	24.279
beta2_pH[11,3]	-1.593	7.256	-19.331	-1.457	15.253
beta2_pH[12,3]	-1.627	7.249	-18.687	-1.711	15.377
beta2_pH[13,3]	-1.824	7.250	-18.941	-1.878	15.385
beta2_pH[14,3]	-1.880	7.223	-19.061	-1.885	14.951
beta2_pH[15,3]	-1.952	7.289	-19.202	-1.954	15.439
beta2_pH[16,3]	-1.913	7.301	-19.287	-1.944	15.119
beta3_pH[1,1]	29.578	8.218	18.394	27.836	44.831
beta3_pH[2,1]	33.912	7.666	18.975	32.974	45.577
beta3_pH[3,1]	30.375	7.452	18.555	30.935	44.562
beta3_pH[4,1]	30.214	7.930	18.473	30.061	45.193
beta3_pH[5,1]	29.191	7.505	18.477	28.407	44.499
beta3_pH[6,1]	29.815	7.935	18.406	28.596	44.771
beta3_pH[7,1]	34.404	9.386	18.602	36.009	44.825
beta3_pH[8,1]	27.341	6.482	18.363	26.991	42.850
beta3_pH[9,1]	29.368	8.027	18.389	27.887	44.770
beta3_pH[10,1]	30.358	8.396	18.475	29.524	44.838
beta3_pH[11,1]	37.845	5.045	29.467	38.178	45.572
beta3_pH[12,1]	36.819	4.893	29.371	36.461	45.518
beta3_pH[13,1]	36.601	4.956	29.299	36.249	45.420
beta3_pH[14,1]	35.027	4.791	29.178	33.632	45.278
beta3_pH[15,1]	34.485	3.852	29.262	33.811	44.178
beta3_pH[16,1]	35.883	4.560	29.315	35.560	44.972
beta3_pH[1,2]	30.082	8.016	18.483	29.096	44.989
beta3_pH[2,2]	29.930	7.900	18.439	29.219	44.994
beta3_pH[3,2]	29.709	7.827	18.550	28.635	44.669
beta3_pH[4,2]	30.039	7.880	18.487	29.114	44.708
beta3_pH[5,2]	29.715	7.852	18.459	28.736	44.746
beta3_pH[6,2]	29.868	7.859	18.516	28.739	44.797
beta3_pH[7,2]	30.116	8.067	18.391	29.247	44.901
beta3_pH[8,2]	30.046	7.951	18.566	28.977	44.917
beta3_pH[9,2]	29.935	8.095	18.392	28.795	44.938
beta3_pH[10,2]	29.741	8.003	18.527	28.578	45.113
beta3_pH[11,2]	42.356	2.842	33.412	43.354	43.809
beta3_pH[12,2]	42.782	1.506	37.724	43.135	43.734
beta3_pH[13,2]	43.549	1.586	40.413	43.886	44.094
beta3_pH[14,2]	43.168	1.103	42.207	43.268	43.855
beta3_pH[15,2]	42.920	1.977	35.445	43.372	43.795
beta3_pH[16,2]	43.107	1.990	36.019	43.487	43.855
beta3_pH[1,3]	38.925	4.117	30.104	39.172	45.642
beta3_pH[2,3]	30.403	8.042	18.498	29.756	44.992
beta3_pH[3,3]	30.259	8.011	18.484	29.495	44.923
beta3_pH[4,3]	30.308	8.096	18.440	29.311	45.057
beta3_pH[5,3]	40.225	3.895	31.936	41.478	45.335
beta3_pH[6,3]	37.063	4.644	31.182	35.426	45.526
beta3_pH[7,3]	38.177	4.352	31.339	37.895	45.562
beta3_pH[8,3]	41.439	0.634	40.152	41.458	42.475
beta3_pH[9,3]	33.541	0.646	31.776	33.591	34.744
beta3_pH[10,3]	35.740	1.030	33.053	35.996	36.984
beta3_pH[11,3]	39.741	4.007	29.820	41.343	44.552
beta3_pH[12,3]	39.838	3.870	29.832	41.528	44.573
beta3_pH[13,3]	40.419	4.485	29.816	42.473	45.373
beta3_pH[14,3]	39.428	3.682	29.950	40.868	44.506
beta3_pH[15,3]	39.992	4.417	29.823	42.095	44.972
beta3_pH[16,3]	40.394	4.541	29.751	42.699	45.003
beta0_pelagic[1]	2.201	0.129	1.944	2.199	2.455
beta0_pelagic[2]	1.444	0.124	1.186	1.457	1.648
beta0_pelagic[3]	0.192	0.258	-0.434	0.223	0.637
beta0_pelagic[4]	0.072	0.690	-1.836	0.251	0.870
beta0_pelagic[5]	1.152	0.254	0.644	1.155	1.652
beta0_pelagic[6]	1.392	0.296	0.739	1.429	1.883
beta0_pelagic[7]	1.630	0.215	1.219	1.616	2.079
beta0_pelagic[8]	1.722	0.204	1.286	1.726	2.134
beta0_pelagic[9]	2.457	0.316	1.848	2.450	3.056
beta0_pelagic[10]	2.480	0.215	2.033	2.484	2.911
beta0_pelagic[11]	-0.321	0.507	-1.150	-0.427	0.472
beta0_pelagic[12]	1.667	0.156	1.363	1.671	1.952
beta0_pelagic[13]	0.141	0.265	-0.493	0.204	0.520
beta0_pelagic[14]	-0.085	0.231	-0.512	-0.096	0.379
beta0_pelagic[15]	-0.341	0.162	-0.673	-0.328	-0.037
beta0_pelagic[16]	0.184	0.251	-0.407	0.211	0.598
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	1.028	0.553	0.412	0.880	2.483
beta1_pelagic[4]	1.484	1.340	0.055	0.959	5.282
beta1_pelagic[5]	-0.067	0.306	-0.674	-0.070	0.521
beta1_pelagic[6]	-0.074	0.517	-0.957	-0.130	0.873
beta1_pelagic[7]	-0.014	0.314	-0.624	-0.021	0.611
beta1_pelagic[8]	-0.015	0.272	-0.551	-0.019	0.532
beta1_pelagic[9]	0.228	0.482	-0.763	0.338	0.970
beta1_pelagic[10]	0.068	0.281	-0.490	0.071	0.590
beta1_pelagic[11]	2.973	0.462	2.278	2.893	4.219
beta1_pelagic[12]	2.814	0.325	2.211	2.804	3.492
beta1_pelagic[13]	3.083	0.688	1.814	2.994	4.424
beta1_pelagic[14]	4.101	0.814	3.001	3.919	5.954
beta1_pelagic[15]	3.033	0.424	2.467	2.945	4.359
beta1_pelagic[16]	3.509	0.475	2.789	3.470	4.651
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	2.155	4.155	0.063	0.482	16.337
beta2_pelagic[4]	2.411	4.532	0.024	0.548	18.482
beta2_pelagic[5]	-0.013	0.683	-1.486	-0.011	1.411
beta2_pelagic[6]	-0.074	0.705	-1.438	-0.135	1.346
beta2_pelagic[7]	0.032	0.663	-1.359	0.043	1.357
beta2_pelagic[8]	-0.059	0.651	-1.388	-0.051	1.293
beta2_pelagic[9]	0.207	0.681	-1.320	0.264	1.523
beta2_pelagic[10]	0.058	0.643	-1.278	0.052	1.478
beta2_pelagic[11]	1.014	1.776	0.139	0.246	6.313
beta2_pelagic[12]	3.995	3.805	0.758	2.880	14.237
beta2_pelagic[13]	0.582	1.095	0.146	0.369	2.126
beta2_pelagic[14]	0.323	0.131	0.196	0.289	0.632
beta2_pelagic[15]	3.339	3.216	0.500	2.228	12.083
beta2_pelagic[16]	1.883	3.218	0.244	0.720	11.490
beta3_pelagic[1]	29.864	7.880	18.534	28.803	44.948
beta3_pelagic[2]	29.965	7.779	18.453	29.322	44.567
beta3_pelagic[3]	31.126	4.535	23.869	30.535	41.629
beta3_pelagic[4]	27.177	5.557	18.974	26.182	43.572
beta3_pelagic[5]	29.963	8.204	18.439	28.472	45.185
beta3_pelagic[6]	31.569	6.275	19.279	31.339	43.807
beta3_pelagic[7]	30.007	7.777	18.576	28.867	44.922
beta3_pelagic[8]	29.900	8.144	18.403	28.636	45.043
beta3_pelagic[9]	30.676	6.049	19.255	30.590	43.101
beta3_pelagic[10]	29.409	8.060	18.394	27.709	44.861
beta3_pelagic[11]	37.296	4.396	30.829	35.749	43.506
beta3_pelagic[12]	43.441	0.311	42.830	43.432	44.055
beta3_pelagic[13]	42.318	1.476	39.655	42.386	45.128
beta3_pelagic[14]	41.962	1.790	37.787	42.070	45.223
beta3_pelagic[15]	42.966	0.429	42.019	43.019	43.727
beta3_pelagic[16]	42.274	1.154	39.235	42.567	43.701
mu_beta0_pelagic[1]	0.911	0.906	-1.087	0.964	2.650
mu_beta0_pelagic[2]	1.775	0.407	0.914	1.791	2.547
mu_beta0_pelagic[3]	0.200	0.498	-0.818	0.216	1.123
tau_beta0_pelagic[1]	0.762	0.804	0.062	0.495	3.079
tau_beta0_pelagic[2]	2.736	2.786	0.246	1.924	10.372
tau_beta0_pelagic[3]	1.342	1.054	0.142	1.064	4.107
beta0_yellow[1]	-0.521	0.186	-0.936	-0.511	-0.198
beta0_yellow[2]	0.492	0.148	0.212	0.492	0.772
beta0_yellow[3]	-0.334	0.184	-0.717	-0.326	-0.007
beta0_yellow[4]	0.829	0.291	-0.053	0.891	1.213
beta0_yellow[5]	-0.341	0.351	-1.024	-0.347	0.366
beta0_yellow[6]	1.110	0.169	0.771	1.112	1.439
beta0_yellow[7]	1.016	0.164	0.695	1.017	1.350
beta0_yellow[8]	0.984	0.159	0.670	0.983	1.301
beta0_yellow[9]	0.659	0.161	0.351	0.661	0.975
beta0_yellow[10]	0.598	0.144	0.315	0.595	0.873
beta0_yellow[11]	-1.603	0.557	-2.541	-1.629	-0.664
beta0_yellow[12]	-3.628	0.474	-4.622	-3.620	-2.757
beta0_yellow[13]	-3.952	0.590	-5.150	-3.950	-2.791
beta0_yellow[14]	-1.423	0.817	-2.720	-1.587	-0.048
beta0_yellow[15]	-2.544	0.462	-3.355	-2.551	-1.487
beta0_yellow[16]	-2.003	0.715	-3.207	-2.101	-0.446
beta1_yellow[1]	0.611	0.451	0.005	0.558	1.654
beta1_yellow[2]	1.004	0.263	0.550	0.984	1.539
beta1_yellow[3]	0.724	0.270	0.251	0.711	1.412
beta1_yellow[4]	1.334	0.605	0.628	1.191	3.178
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	1.770	0.555	0.790	1.789	2.661
beta1_yellow[12]	2.431	0.506	1.483	2.421	3.511
beta1_yellow[13]	3.106	0.589	1.993	3.112	4.265
beta1_yellow[14]	1.761	0.834	0.345	1.766	3.649
beta1_yellow[15]	1.874	0.436	0.933	1.849	2.755
beta1_yellow[16]	1.796	0.679	0.343	1.869	2.953
beta2_yellow[1]	-3.176	2.794	-10.347	-2.419	-0.046
beta2_yellow[2]	-2.990	2.436	-9.710	-2.351	-0.271
beta2_yellow[3]	-2.464	2.254	-8.935	-1.921	-0.121
beta2_yellow[4]	-2.902	2.749	-9.631	-2.102	-0.077
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	-3.959	2.332	-10.397	-3.462	-0.940
beta2_yellow[12]	-4.486	2.621	-11.418	-3.879	-1.075
beta2_yellow[13]	-4.340	2.384	-10.343	-3.757	-1.414
beta2_yellow[14]	-3.523	2.829	-10.625	-3.098	-0.058
beta2_yellow[15]	-4.136	2.612	-10.747	-3.523	-0.838
beta2_yellow[16]	-4.532	2.632	-11.166	-3.979	-0.972
beta3_yellow[1]	26.808	7.186	18.352	24.050	43.903
beta3_yellow[2]	29.408	1.691	26.813	29.082	33.251
beta3_yellow[3]	32.858	3.143	25.226	32.859	39.013
beta3_yellow[4]	29.010	2.962	24.458	27.981	35.629
beta3_yellow[5]	29.871	7.886	18.503	28.808	44.713
beta3_yellow[6]	29.969	7.950	18.457	29.092	44.898
beta3_yellow[7]	29.836	8.025	18.383	28.692	45.002
beta3_yellow[8]	29.901	7.913	18.494	28.798	44.856
beta3_yellow[9]	29.841	7.937	18.448	28.701	44.974
beta3_yellow[10]	30.012	7.908	18.461	28.973	44.872
beta3_yellow[11]	45.061	0.711	43.271	45.189	45.958
beta3_yellow[12]	43.268	0.425	42.404	43.252	44.097
beta3_yellow[13]	44.921	0.395	43.982	44.991	45.568
beta3_yellow[14]	40.996	4.536	33.186	43.569	45.792
beta3_yellow[15]	44.923	0.956	43.257	45.007	45.953
beta3_yellow[16]	43.752	2.627	34.368	44.432	45.842
mu_beta0_yellow[1]	0.106	0.538	-1.008	0.106	1.283
mu_beta0_yellow[2]	0.640	0.330	-0.061	0.656	1.260
mu_beta0_yellow[3]	-2.069	0.804	-3.348	-2.165	-0.248
tau_beta0_yellow[1]	1.757	1.840	0.090	1.197	6.822
tau_beta0_yellow[2]	3.383	4.075	0.304	2.286	13.562
tau_beta0_yellow[3]	0.841	1.236	0.069	0.478	3.793
beta0_black[1]	-0.074	0.160	-0.389	-0.077	0.239
beta0_black[2]	1.916	0.130	1.655	1.913	2.174
beta0_black[3]	1.318	0.138	1.055	1.318	1.585
beta0_black[4]	2.432	0.134	2.166	2.432	2.690
beta0_black[5]	4.735	2.072	1.887	4.306	10.064
beta0_black[6]	4.737	1.972	2.286	4.240	9.982
beta0_black[7]	3.829	1.989	1.575	3.321	9.353
beta0_black[8]	0.943	0.209	0.552	0.941	1.364
beta0_black[9]	2.612	0.233	2.157	2.615	3.074
beta0_black[10]	1.466	0.137	1.211	1.461	1.736
beta0_black[11]	3.489	0.154	3.185	3.490	3.785
beta0_black[12]	4.876	0.177	4.522	4.873	5.223
beta0_black[13]	-0.110	0.244	-0.591	-0.111	0.372
beta0_black[14]	2.853	0.160	2.546	2.856	3.158
beta0_black[15]	1.294	0.161	0.978	1.295	1.608
beta0_black[16]	4.273	0.161	3.969	4.271	4.589
beta2_black[1]	8.365	10.706	0.517	3.592	41.926
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-1.860	1.549	-6.314	-1.362	-0.386
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	41.787	1.224	39.876	41.960	43.361
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	39.195	0.802	37.328	39.292	40.526
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.267	0.201	-0.665	-0.267	0.131
beta4_black[2]	0.238	0.187	-0.130	0.238	0.600
beta4_black[3]	-0.935	0.200	-1.326	-0.938	-0.542
beta4_black[4]	0.430	0.218	0.001	0.432	0.860
beta4_black[5]	0.564	1.351	-1.457	0.333	3.830
beta4_black[6]	0.531	1.282	-1.318	0.326	3.697
beta4_black[7]	0.458	1.233	-1.313	0.270	3.558
beta4_black[8]	-0.226	0.318	-0.865	-0.213	0.390
beta4_black[9]	0.845	0.801	-0.257	0.692	2.824
beta4_black[10]	0.047	0.187	-0.336	0.050	0.409
beta4_black[11]	-0.697	0.216	-1.094	-0.703	-0.261
beta4_black[12]	0.167	0.324	-0.452	0.156	0.839
beta4_black[13]	-1.185	0.227	-1.653	-1.184	-0.747
beta4_black[14]	-0.178	0.242	-0.658	-0.179	0.290
beta4_black[15]	-0.886	0.217	-1.321	-0.883	-0.455
beta4_black[16]	-0.592	0.231	-1.031	-0.593	-0.120
mu_beta0_black[1]	1.277	0.946	-0.893	1.338	3.075
mu_beta0_black[2]	2.726	1.092	0.646	2.644	5.198
mu_beta0_black[3]	2.505	0.952	0.512	2.529	4.336
tau_beta0_black[1]	0.622	0.603	0.056	0.430	2.270
tau_beta0_black[2]	0.423	0.613	0.046	0.224	1.996
tau_beta0_black[3]	0.233	0.152	0.049	0.195	0.625
beta0_dsr[11]	-4.391	2.518	-10.248	-2.948	-2.326
beta0_dsr[12]	4.558	0.287	4.023	4.549	5.146
beta0_dsr[13]	-2.166	1.327	-5.667	-1.575	-0.744
beta0_dsr[14]	-3.988	0.501	-5.008	-4.006	-2.989
beta0_dsr[15]	-2.121	0.673	-4.567	-1.991	-1.366
beta0_dsr[16]	-3.068	0.380	-3.833	-3.068	-2.307
beta1_dsr[11]	9.216	6.396	4.251	4.950	20.516
beta1_dsr[12]	14.397	38.619	2.300	5.841	122.988
beta1_dsr[13]	4.139	1.984	2.266	3.153	9.571
beta1_dsr[14]	6.652	0.533	5.615	6.663	7.724
beta1_dsr[15]	3.559	0.712	2.826	3.407	6.082
beta1_dsr[16]	5.892	0.394	5.106	5.891	6.661
beta2_dsr[11]	-5.493	4.310	-13.033	-6.396	-0.058
beta2_dsr[12]	-6.028	2.825	-12.354	-5.831	-1.391
beta2_dsr[13]	-3.601	3.510	-10.867	-3.020	-0.102
beta2_dsr[14]	-5.099	2.570	-10.913	-4.552	-1.712
beta2_dsr[15]	-6.717	3.003	-13.108	-6.614	-0.524
beta2_dsr[16]	-7.589	2.523	-13.320	-7.242	-3.705
beta3_dsr[11]	41.257	3.809	32.361	43.380	43.808
beta3_dsr[12]	33.791	0.840	31.576	34.003	34.799
beta3_dsr[13]	43.489	0.988	41.456	43.268	45.759
beta3_dsr[14]	43.407	0.229	43.087	43.366	43.925
beta3_dsr[15]	43.626	0.468	43.171	43.535	45.391
beta3_dsr[16]	43.446	0.159	43.178	43.434	43.771
beta4_dsr[11]	0.570	0.228	0.139	0.561	1.026
beta4_dsr[12]	0.242	0.447	-0.655	0.239	1.119
beta4_dsr[13]	-0.172	0.230	-0.628	-0.170	0.267
beta4_dsr[14]	0.157	0.253	-0.353	0.166	0.626
beta4_dsr[15]	0.706	0.225	0.270	0.708	1.154
beta4_dsr[16]	0.153	0.230	-0.314	0.155	0.602
beta0_slope[11]	-1.841	0.145	-2.121	-1.846	-1.551
beta0_slope[12]	-4.496	0.272	-5.064	-4.486	-3.984
beta0_slope[13]	-1.343	0.186	-1.787	-1.328	-1.036
beta0_slope[14]	-2.678	0.171	-3.009	-2.682	-2.347
beta0_slope[15]	-1.350	0.147	-1.641	-1.352	-1.062
beta0_slope[16]	-2.726	0.156	-3.028	-2.729	-2.416
beta1_slope[11]	4.488	0.227	4.040	4.490	4.923
beta1_slope[12]	4.001	0.490	3.090	3.994	4.902
beta1_slope[13]	2.714	0.444	2.193	2.643	4.020
beta1_slope[14]	6.339	0.412	5.543	6.335	7.174
beta1_slope[15]	3.019	0.216	2.614	3.017	3.435
beta1_slope[16]	5.281	0.286	4.735	5.285	5.840
beta2_slope[11]	8.608	2.287	5.048	8.275	13.927
beta2_slope[12]	6.565	3.009	1.086	6.633	12.804
beta2_slope[13]	5.449	3.041	0.365	5.424	11.647
beta2_slope[14]	6.446	2.665	2.219	6.257	12.427
beta2_slope[15]	8.064	2.226	4.621	7.779	12.985
beta2_slope[16]	7.630	2.146	4.098	7.342	12.644
beta3_slope[11]	43.460	0.136	43.212	43.458	43.732
beta3_slope[12]	43.338	0.295	42.806	43.295	43.932
beta3_slope[13]	43.467	0.387	42.906	43.421	44.028
beta3_slope[14]	43.271	0.141	43.094	43.237	43.628
beta3_slope[15]	43.497	0.159	43.206	43.495	43.798
beta3_slope[16]	43.375	0.140	43.162	43.352	43.690
beta4_slope[11]	-0.735	0.168	-1.076	-0.731	-0.411
beta4_slope[12]	-1.153	0.462	-2.166	-1.119	-0.363
beta4_slope[13]	0.082	0.164	-0.227	0.081	0.410
beta4_slope[14]	-0.088	0.198	-0.478	-0.091	0.308
beta4_slope[15]	-0.757	0.160	-1.069	-0.757	-0.449
beta4_slope[16]	-0.171	0.177	-0.513	-0.170	0.177
sigma_H[1]	0.200	0.050	0.109	0.199	0.308
sigma_H[2]	0.173	0.029	0.121	0.172	0.237
sigma_H[3]	0.200	0.043	0.125	0.197	0.294
sigma_H[4]	0.388	0.073	0.270	0.380	0.554
sigma_H[5]	1.004	0.232	0.595	0.989	1.477
sigma_H[6]	0.293	0.186	0.020	0.268	0.727
sigma_H[7]	0.286	0.054	0.201	0.279	0.408
sigma_H[8]	0.449	0.116	0.297	0.429	0.703
sigma_H[9]	0.430	0.093	0.292	0.415	0.655
sigma_H[10]	0.226	0.045	0.152	0.222	0.324
sigma_H[11]	0.282	0.047	0.199	0.279	0.385
sigma_H[12]	0.453	0.173	0.208	0.437	0.786
sigma_H[13]	0.201	0.036	0.138	0.198	0.283
sigma_H[14]	0.455	0.090	0.304	0.448	0.657
sigma_H[15]	0.250	0.042	0.179	0.247	0.342
sigma_H[16]	0.252	0.048	0.174	0.246	0.358
lambda_H[1]	2.923	4.118	0.145	1.545	14.292
lambda_H[2]	9.491	8.356	0.908	6.977	30.838
lambda_H[3]	6.857	9.553	0.336	3.644	32.814
lambda_H[4]	0.007	0.005	0.001	0.006	0.019
lambda_H[5]	2.075	5.718	0.014	0.338	14.521
lambda_H[6]	7.381	12.731	0.011	1.626	42.047
lambda_H[7]	0.014	0.010	0.002	0.012	0.040
lambda_H[8]	4.868	8.476	0.000	1.243	29.625
lambda_H[9]	0.019	0.013	0.003	0.016	0.052
lambda_H[10]	0.406	1.380	0.035	0.198	1.703
lambda_H[11]	0.374	0.527	0.014	0.211	1.729
lambda_H[12]	5.842	7.551	0.274	3.486	26.336
lambda_H[13]	4.059	3.579	0.352	3.113	13.748
lambda_H[14]	3.361	3.707	0.286	2.265	14.068
lambda_H[15]	0.043	0.270	0.004	0.019	0.155
lambda_H[16]	3.377	4.252	0.169	2.086	13.855
mu_lambda_H[1]	4.459	1.931	1.304	4.254	8.618
mu_lambda_H[2]	3.545	1.968	0.276	3.404	7.659
mu_lambda_H[3]	3.823	1.871	0.952	3.560	8.034
sigma_lambda_H[1]	8.912	4.370	2.215	8.316	18.566
sigma_lambda_H[2]	7.988	4.817	0.434	7.403	18.141
sigma_lambda_H[3]	6.457	3.902	1.172	5.597	16.086
beta_H[1,1]	6.792	1.105	4.161	6.977	8.471
beta_H[2,1]	9.872	0.456	8.905	9.885	10.735
beta_H[3,1]	7.998	0.744	6.262	8.090	9.204
beta_H[4,1]	10.703	7.674	-4.648	10.772	25.492
beta_H[5,1]	-0.025	3.121	-6.458	0.152	6.328
beta_H[6,1]	3.323	3.651	-6.316	4.668	7.495
beta_H[7,1]	1.386	5.612	-10.726	1.707	11.543
beta_H[8,1]	15.271	21.979	-2.458	2.104	62.646
beta_H[9,1]	13.818	5.441	3.616	13.538	25.498
beta_H[10,1]	7.154	1.705	3.721	7.208	10.564
beta_H[11,1]	6.098	3.167	-1.520	6.928	10.253
beta_H[12,1]	2.566	0.949	0.879	2.490	4.686
beta_H[13,1]	9.037	0.811	7.304	9.111	10.382
beta_H[14,1]	2.145	0.960	0.139	2.142	4.006
beta_H[15,1]	-5.171	4.081	-12.364	-5.420	3.860
beta_H[16,1]	3.615	1.632	0.277	3.681	6.588
beta_H[1,2]	7.920	0.247	7.404	7.934	8.375
beta_H[2,2]	10.042	0.130	9.783	10.043	10.294
beta_H[3,2]	8.957	0.196	8.559	8.957	9.347
beta_H[4,2]	3.095	1.444	0.322	3.023	6.091
beta_H[5,2]	1.961	1.059	-0.138	1.993	3.962
beta_H[6,2]	5.814	0.973	3.521	5.959	7.322
beta_H[7,2]	2.378	1.077	0.434	2.311	4.689
beta_H[8,2]	-0.297	5.120	-10.735	2.682	4.284
beta_H[9,2]	2.954	1.015	0.920	2.955	4.913
beta_H[10,2]	8.162	0.350	7.402	8.177	8.814
beta_H[11,2]	9.592	0.571	8.786	9.455	10.961
beta_H[12,2]	3.965	0.352	3.285	3.947	4.668
beta_H[13,2]	9.166	0.222	8.741	9.161	9.611
beta_H[14,2]	4.064	0.343	3.390	4.060	4.740
beta_H[15,2]	11.205	0.728	9.716	11.249	12.550
beta_H[16,2]	5.444	0.811	3.795	5.439	6.966
beta_H[1,3]	8.557	0.247	8.114	8.546	9.069
beta_H[2,3]	10.131	0.109	9.919	10.127	10.361
beta_H[3,3]	9.656	0.161	9.354	9.655	9.981
beta_H[4,3]	-1.817	0.927	-3.614	-1.834	0.018
beta_H[5,3]	4.167	0.743	2.623	4.199	5.595
beta_H[6,3]	7.986	1.199	6.461	7.576	10.677
beta_H[7,3]	-2.474	0.661	-3.798	-2.468	-1.207
beta_H[8,3]	6.935	2.323	4.751	5.560	11.571
beta_H[9,3]	-1.939	0.694	-3.283	-1.941	-0.536
beta_H[10,3]	8.865	0.286	8.319	8.865	9.433
beta_H[11,3]	8.668	0.266	8.100	8.689	9.132
beta_H[12,3]	5.370	0.289	4.714	5.397	5.872
beta_H[13,3]	9.036	0.169	8.717	9.033	9.369
beta_H[14,3]	5.861	0.265	5.293	5.872	6.351
beta_H[15,3]	10.488	0.328	9.854	10.486	11.126
beta_H[16,3]	7.400	0.427	6.470	7.438	8.128
beta_H[1,4]	8.309	0.177	7.926	8.317	8.621
beta_H[2,4]	10.207	0.107	9.976	10.213	10.404
beta_H[3,4]	10.165	0.162	9.819	10.178	10.453
beta_H[4,4]	11.714	0.424	10.853	11.720	12.520
beta_H[5,4]	6.100	0.949	4.564	5.978	8.200
beta_H[6,4]	7.265	0.795	5.322	7.477	8.362
beta_H[7,4]	8.195	0.341	7.502	8.200	8.838
beta_H[8,4]	6.183	0.877	4.283	6.606	7.143
beta_H[9,4]	6.993	0.399	6.223	6.990	7.800
beta_H[10,4]	7.828	0.256	7.366	7.821	8.381
beta_H[11,4]	9.426	0.200	9.035	9.429	9.808
beta_H[12,4]	7.155	0.211	6.738	7.153	7.578
beta_H[13,4]	9.152	0.142	8.874	9.153	9.419
beta_H[14,4]	7.823	0.211	7.403	7.821	8.235
beta_H[15,4]	9.496	0.240	9.020	9.497	9.950
beta_H[16,4]	9.216	0.179	8.901	9.205	9.590
beta_H[1,5]	8.995	0.147	8.698	9.002	9.279
beta_H[2,5]	10.790	0.091	10.617	10.789	10.979
beta_H[3,5]	10.907	0.164	10.617	10.899	11.241
beta_H[4,5]	8.430	0.430	7.608	8.417	9.300
beta_H[5,5]	5.072	0.833	3.141	5.233	6.308
beta_H[6,5]	8.668	0.574	7.852	8.547	10.035
beta_H[7,5]	6.821	0.327	6.190	6.818	7.471
beta_H[8,5]	8.602	0.663	7.842	8.323	10.142
beta_H[9,5]	8.284	0.408	7.481	8.289	9.048
beta_H[10,5]	10.078	0.245	9.585	10.082	10.554
beta_H[11,5]	11.472	0.229	11.027	11.473	11.918
beta_H[12,5]	8.469	0.194	8.090	8.471	8.852
beta_H[13,5]	10.038	0.121	9.800	10.037	10.283
beta_H[14,5]	9.195	0.209	8.784	9.188	9.618
beta_H[15,5]	11.166	0.240	10.712	11.164	11.657
beta_H[16,5]	9.983	0.145	9.680	9.987	10.258
beta_H[1,6]	10.191	0.189	9.872	10.176	10.618
beta_H[2,6]	11.504	0.104	11.298	11.501	11.710
beta_H[3,6]	10.814	0.156	10.472	10.821	11.091
beta_H[4,6]	12.862	0.763	11.279	12.882	14.335
beta_H[5,6]	6.072	0.744	4.734	6.047	7.748
beta_H[6,6]	8.738	0.563	7.268	8.800	9.623
beta_H[7,6]	9.816	0.552	8.705	9.807	10.865
beta_H[8,6]	8.974	0.948	6.660	9.379	9.974
beta_H[9,6]	8.394	0.668	7.094	8.383	9.700
beta_H[10,6]	9.556	0.326	8.839	9.582	10.143
beta_H[11,6]	10.875	0.320	10.176	10.898	11.458
beta_H[12,6]	9.379	0.250	8.921	9.375	9.887
beta_H[13,6]	11.074	0.150	10.798	11.070	11.375
beta_H[14,6]	9.798	0.262	9.245	9.795	10.301
beta_H[15,6]	10.869	0.421	10.015	10.875	11.675
beta_H[16,6]	10.651	0.178	10.279	10.659	10.989
beta_H[1,7]	10.852	0.907	8.549	10.966	12.247
beta_H[2,7]	12.217	0.413	11.377	12.214	13.039
beta_H[3,7]	10.577	0.650	9.092	10.651	11.679
beta_H[4,7]	2.565	3.868	-5.061	2.508	10.471
beta_H[5,7]	6.994	2.587	2.439	6.802	12.934
beta_H[6,7]	9.202	2.121	4.749	9.268	14.268
beta_H[7,7]	10.764	2.753	5.456	10.749	16.138
beta_H[8,7]	13.076	4.033	9.129	11.231	23.534
beta_H[9,7]	4.629	3.376	-2.169	4.715	11.399
beta_H[10,7]	9.831	1.503	6.984	9.750	13.165
beta_H[11,7]	10.894	1.587	7.952	10.772	14.419
beta_H[12,7]	10.090	0.840	8.236	10.134	11.544
beta_H[13,7]	11.750	0.682	10.198	11.810	12.891
beta_H[14,7]	10.339	0.846	8.490	10.361	11.875
beta_H[15,7]	11.991	2.162	7.683	11.952	16.248
beta_H[16,7]	11.713	0.797	10.383	11.612	13.579
beta0_H[1]	8.989	13.806	-18.290	8.880	38.688
beta0_H[2]	10.664	5.721	-1.721	10.698	22.280
beta0_H[3]	9.766	9.258	-8.830	10.016	28.137
beta0_H[4]	5.589	175.877	-352.049	6.143	352.718
beta0_H[5]	4.842	41.131	-76.474	4.520	91.014
beta0_H[6]	7.812	42.009	-79.174	7.680	105.578
beta0_H[7]	6.854	128.153	-254.628	7.076	254.714
beta0_H[8]	12.658	216.995	-498.350	6.862	557.754
beta0_H[9]	7.981	110.221	-223.129	6.225	225.032
beta0_H[10]	9.460	33.189	-56.535	9.013	76.331
beta0_H[11]	9.741	43.125	-86.106	9.975	98.449
beta0_H[12]	6.601	9.412	-12.236	6.729	25.131
beta0_H[13]	10.010	9.735	-8.406	10.102	29.294
beta0_H[14]	6.957	10.407	-14.772	7.017	26.635
beta0_H[15]	10.912	104.572	-194.583	8.610	225.614
beta0_H[16]	8.138	12.578	-16.338	8.281	31.889